The authors gratefully acknowledge the financial support of DARPA through the Materials with Controlled Microstructural Architecture program and of JRG's NASA Early Career grants. The authors are grateful to Ramathasan Thevamaran and Ladan Salari for helping on bulk compression testing, Scott Godfrey for FE simulations, Lucas Meza and Dongchan Jang for fruitful discussions and the Kavli Nanoscience Institute (KNI) at Caltech for providing support and infrastructure.